The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in the ratio of:

1. 1 : 2                           
2. 2 : 3
3. 2 : 1                      
4. 4 : 1

If the angular speed of the earth is doubled, the value of acceleration due to gravity (g) at the north pole

(1) Doubles                   

(2)  Becomes half

(3)  Remains same       

(4)   Becomes zero

Escape velocity of a body of 1 kg mass on a planet is 100 m/sec. Gravitational Potential energy of the body at the planet is -

(1)   – 5000 J                     

(2)  – 1000 J

(3)   – 2400 J                      

(4)  5000 J

At the surface of a certain planet, acceleration due to gravity is one-quarter of that on earth. If a brass ball is transported to this planet, then which one of the following statements is not correct?

Weight of 1 kg becomes 1/6 kg on moon. If radius of moon is $1.768\times {10}^{6}m$, then the mass of moon will be -

(a) $1.99\times {10}^{30}kg$                        (b) $7.56\times {10}^{22}kg$

 (c) $5.98\times {10}^{24}kg$                       (d) $7.65\times {10}^{22}kg$

Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities same, then

(1)  g decreases by 2% and K decreases by 4%

(2)  g decreases by 4% and K increases by 2%

(3)  g increases by 4% and K increases by 4%

(4)  g decreases by 4% and K increases by 4%

The distance between centre of the earth and moon is 384000 km. If the mass of the earth is $6\times {10}^{24} kg$ and $G=6.66\times {10}^{-11} N{m}^2/k{g}^2$ . The speed of the moon is nearly -

(a) 1 km/sec                          (b) 4 km/sec

(c) 8 km/sec                          (d) 11.2 km/sec

A body is projected vertically upwards from the surface of a planet of radius \(R\) with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. \(\frac{R}{3}\)
2. \(\frac{R}{2}\)
3. \(\frac{R}{4}\)
4. \(\frac{R}{5}\)

A satellite is launched into a circular orbit of radius \(R\) around the Earth while a second satellite is launched into an orbit of radius \(1.02~\text{R}\). The percentage difference in the time periods of the two satellites is: 

Distance of geostationary satellite from the center of the Earth $(R_e=6400 km)$ in terms of $R_e$ is-

(1) $13.76 R_e$                        

(2) $10.76 R_e$

(3) $6.59 R_e$                            

(4) $2.56 R_e$